Page 507 - Mathematical Techniques of Fractional Order Systems

494 Mathematical Techniques of Fractional Order Systems

16.5 CONCLUSIONS
In this chapter, a chaotic system with seven terms has been studied. The sys-
tem is different from a conventional system because it includes signum and
exponential nonlinear terms. It is interesting that the system is special
because there is the presence of an infinite number of equilibrium points. By
using phase portraits, Poincare ´ map, bifurcation diagram, and Lyapunov
exponents, we have investigated the system’s dynamics. We have observed
chaos and coexisting attractors in such a system. In addition, we have pro-
posed an adaptive control for antisynchronization of chaotic systems with
infinite equilibria. Fractional order form of the system with infinite equilibria
can exhibit chaotic and point attractors. Practical applications of the new sys-
tem will be discovered in our future works.

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